Lower inflation doesn't mean lower prices - which we need, and/or higher wages - it means prices are going up a little more slowly. Pointing at a $9 jar of mayonnaise with an "I did this" isn't going to win many people over.
It shouldn't mean lower prices; deflation is bad, we just want a low rate of inflation. What we do want is for wages to outpace that, and for the past couple of years, they have for people at the lower end of the scale (which is also good)